In the AP (-38,-25,-12,\ldots), what is the first term greater than (300)?

Correct answer: 313

Here, the first term is \(a=-38\) and the common difference is \(d=13\). Thus, \(a_n=-38+13(n-1)=13n-51\). For \(a_n>300\), we get \(13n-51>300\), so \(n>27\). The least integer value is \(n=28\), and \(a_{28}=313\). Note that 300 is not itself a term of the AP, so 313 is the correct answer. Exam tip: for “greater than,” use \(>\) and then take the least possible integer value of \(n\).